Uma formulação multiescala não linear e descontínua para problemas de convecção-difusão-reação

Enéas Mendes de Jesus; Isaac Pinheiro dos Santos

doi:10.35819/remat2024v10iespecialid7088

Autores/as

Enéas Mendes de Jesus Instituto Federal de Educação, Ciência e Tecnologia do Espírito Santo (IFES), Campus Piúma, Piúma, ES; Universidade Federal do Espírito Santo (UFES), Vitória, ES, Brasil https://orcid.org/0000-0002-2384-3831
Isaac Pinheiro dos Santos Universidade Federal do Espírito Santo (UFES), Campus de São Mateus, São Mateus, ES, Brasil https://orcid.org/0000-0001-8524-0393

DOI:

https://doi.org/10.35819/remat2024v10iespecialid7088

Palabras clave:

Galerkin discontinuo, difusión artificial, convección-difusión-reacción, funciones burbuja, métodos multiescala

Resumen

Este trabajo presenta una formulación de Galerkin discontinua multiescala y no lineal con el objetivo de resolver problemas de convección-difusión-reacción. Considerando una descomposición del espacio de aproximación en dos escalas, macro y micro, el nuevo método introduce un operador no lineal de difusión artificial en ambas escalas de discretización, mientras utiliza el enfoque discontinuo solo en la macro escala. La microescala se modela a través de funciones burbuja (funciones polinomiales que se anulan en la frontera de los elementos), permitiendo la aplicación del proceso de condensación estática en cada elemento. La discretización del modelo numérico resulta en un sistema global de ecuaciones asociado a los puntos nodales solo de la macroescala. Para evaluar las propiedades de estabilidad y convergencia del esquema propuesto, se realizaron algunos experimentos numéricos y se compararon con el método de Galerkin discontinuo clásico. La formulación propuesta se mostró eficiente en la eliminación de las oscilaciones espurias que aparecen en regiones de gradientes elevados en problemas con convección/reacción dominantes. Además, el método presentó tasas óptimas de convergencia.

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Biografía del autor/a

Enéas Mendes de Jesus, Instituto Federal de Educação, Ciência e Tecnologia do Espírito Santo (IFES), Campus Piúma, Piúma, ES; Universidade Federal do Espírito Santo (UFES), Vitória, ES, Brasil

http://lattes.cnpq.br/4180558774113196
Isaac Pinheiro dos Santos, Universidade Federal do Espírito Santo (UFES), Campus de São Mateus, São Mateus, ES, Brasil

http://lattes.cnpq.br/3793156690673506

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